L. Campos, L.G. Farah, and J. Murphy,
Threshold solutions for the 3d cubic INLS: the energy-critical case. Submitted.
[arXiv]
L. Campos, L.G. Farah, and J. Murphy,
Threshold solutions for the 3d cubic INLS: the energy-subcritical case. Submitted.
[arXiv]
L. Baker and J. Murphy,
Scattering for the 1d NLS with inhomogeneous nonlinearities. Submitted.
[arXiv]
Z. Ma, C. Miao, J. Murphy, and J. Zheng,
Dynamics of subcritical threshold solutions for the 4d energy-critical NLS. Submitted.
[arXiv]
G. Chen and J. Murphy,
Stability of nonlinear recovery from scattering and modified scattering maps. To appear in Forum. Math.
[arXiv]
J. Murphy and J. Zheng,
Modified scattering for the cubic dispersion-managed NLS. Proc. Amer. Math. Soc.
154 (2026), no. 2, 821–831.
[arXiv] [Journal] [MathSciNet]
A. Ardila, J. Murphy, and J. Zheng,
Threshold dynamics for the 3d radial NLS with combined nonlinearity. J. Differential Equations
453 (2026), 113800.
[arXiv] [Journal] [MathSciNet]
J. Kawakami and J. Murphy,
Small and large data scattering for the dispersion-managed NLS. Discrete Contin. Dyn. Syst.
47 (2026), 256–285.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
Large scale limit for a dispersion-managed NLS. J. Differential Equations
448 (2025), 113830.
[arXiv] [Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
Determination of Schrödinger nonlinearities from the scattering map. Nonlinearity
38, no. 1 (2025).
[arXiv] [Journal] [MathSciNet]
J. Murphy,
A note on averaging and solitons for the dispersion-managed NLS. Nonlinear Differ. Equ. Appl. NoDEA (2024) 31:103.
[arXiv] [Journal] [MathSciNet]
S. Masaki, J. Murphy, and J. Segata,
Global dynamics below excited solitons for the non-radial NLS with potential. Indiana Univ. Math. J.
73 (2024), no. 3, 1097–1205.
[arXiv] [Journal] [MathSciNet]
A. Ardila and J. Murphy,
The cubic-quintic nonlinear Schrödinger equation with inverse-square potential. Nonlinear Differ. Equ. Appl. NoDEA (2024) 31:93.
[arXiv] [Journal] [MathSciNet]
L. Campos, J. Murphy, and T. Van Hoose,
Averaging for the 2d dispersion-managed NLS. Commun. Contemp. Math.
26, no. 7, Article no. 2350030 (2024).
[arXiv] [Journal] [MathSciNet]
G. Chen and J. Murphy,
Recovery of the nonlinearity from the modified scattering map. Int. Math. Res. Not. IMRN 2024, no. 8, 6632–6655.
[arXiv] [Journal] [MathSciNet]
C. Hogan and J. Murphy,
Transmission of fast solitons for the NLS with an external potential. Discrete Contin. Dyn. Syst.
44 (2024), no. 5, 1166–1177.
[arXiv] [Journal] [MathSciNet]
G. Chen and J. Murphy,
Stability estimates for the recovery of the nonlinearity from scattering data. Pure Appl. Anal.
6 (2024), no. 1, 305–317.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
Recovery of a spatially-dependent coefficient from the NLS scattering map. Comm. Partial Differential Equations
48 (2023), no. 7-8, 991–1007.
[arXiv] [Journal] [MathSciNet]
L. Campos and J. Murphy,
Threshold solutions for the intercritical inhomogeneous NLS. SIAM J. Math. Anal
55 (2023), no. 4, 3807–3843.
[arXiv] [Journal] [MathSciNet]
A. Ardila and J. Murphy,
Threshold solutions for the 3d cubic-quintic NLS. Comm. Partial Differential Equations
48 (2023), no. 5, 819–862.
[arXiv] [Journal] [MathSciNet]
R. Killip. J. Murphy, and M. Visan,
The scattering map determines the nonlinearity. Proc. Amer. Math. Soc.
151 (2023), no. 6, 2543–2557.
[arXiv] [Journal] [MathSciNet]
J. Murphy and T. Van Hoose,
Well-posedness and blowup for the dispersion-managed nonlinear Schrödinger equation. Proc. Amer. Math. Soc.
151 (2023), no. 6, 2489–2502.
[arXiv] [Journal] [MathSciNet]
C. Miao, J. Murphy, and J. Zheng,
Threshold scattering for the focusing NLS with a repulsive potential. Indiana Univ. Math. J.
72 (2023), no. 2, 409–453.
[arXiv] [Journal] [MathSciNet]
S. Masaki, J. Murphy, and J. Segata,
Asymptotic stability of solitary waves for the 1d NLS with an attractive delta potential. Discrete Contin. Dyn. Syst.
43 (2023), no. 6, 2137–2185.
[arXiv] [Journal] [MathSciNet]
C. Hogan, J. Murphy, and D. Grow,
Recovery of a cubic nonlinearity for the nonlinear Schrödinger equation. J. Math. Anal. Appl.
522 (2023), no. 1, Article 127016.
[arXiv] [Journal] [MathSciNet]
M. Cardoso, L. G. Farah, C. M. Guzmán, and J. Murphy,
Scattering below the ground state for the intercritical non-radial inhomogeneous NLS. Nonlinear Analysis: Real World Applications, Volume 68, 2022, Article 103687.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
A simple proof of scattering for the intercritical inhomogeneous NLS. Proc. Amer. Math. Soc.
150 (2022), no. 3, 1177–1186.
[arXiv] [Journal] [MathSciNet]
J. Murphy and T. Van Hoose,
Modified scattering for a dispersion-managed nonlinear Schrödinger equation. NoDEA Nonlinear Differential Equations Appl.
29 (2022), no. 1, Art. 1, 11pp.
[arXiv] [Journal] [MathSciNet]
C. Miao, J. Murphy, and J. Zheng,
Scattering for the non-radial inhomogeneous NLS. Math. Res. Lett.
28 (2021), no. 5, 1481–1504.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
A review of modified scattering for the 1d cubic NLS. RIMS Kokyuroku Bessatsu B88 119–146 (2021).
[pdf] [Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
Scattering for the cubic-quintic NLS: crossing the virial threshold. SIAM J. Math. Anal.
53 (2021), no. 5, 5803–5812.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
Threshold scattering for the 2d radial cubic-quintic NLS. Comm. Partial Differential Equations
46 (2021), no. 11, 2213–2234.
[arXiv] [Journal] [MathSciNet]
C. M. Guzmán and J. Murphy,
Scattering for the non-radial energy-critical inhomogeneous NLS. J. Differential Equations
295 (2021), 187–210.
[arXiv] [Journal] [MathSciNet]
J. Murphy and K. Nakanishi,
Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations. Discrete Contin. Dyn. Syst.
41 (2021), no. 3, 1507–1517.
[arXiv] [Journal] [MathSciNet]
B. Dodson, A. Lawrie, D. Mendelson, and J. Murphy,
Scattering for defocusing energy subcritical nonlinear wave equations. Anal. PDE
13 (2020), no. 7, 1995–2090.
[arXiv] [Journal] [MathSciNet]
J. Murphy and Y. Zhang,
Numerical simulations for the energy-supercritical nonlinear wave equation. Nonlinearity
33 (2020), no. 11, 6195–6220.
[arXiv] [Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
Invariance of white noise for KdV on the line. Invent. Math.
222, no. 1, 203–282 (2020).
[arXiv] [Journal] [MathSciNet]
S. Masaki, J. Murphy, and J. Segata,
Stability of small solitary waves for the 1d NLS with an attractive delta potential. Anal. PDE.
13 (2020), no. 4, 1099–1128.
[arXiv] [Journal] [MathSciNet]
C. Miao, J. Murphy, and J. Zheng,
The energy-critical nonlinear wave equation with an inverse-square potential. Ann. Inst. H. Poincaré Anal. Non Linéaire
37 (2020), no. 2, 417–456.
[arXiv] [Journal] [MathSciNet]
A. Arora, B. Dodson, and J. Murphy,
Scattering below the ground state for the 2d radial nonlinear Schrödinger equation. Proc. Amer. Math. Soc.
148 (2020), no. 4, 1653–1663.
[arXiv] [Journal] [MathSciNet]
S. Masaki, J. Murphy, and J. Segata,
Modified scattering for the one-dimensional cubic NLS with a repulsive delta potential. Int. Math. Res. Not. IMRN 2019, no. 24, 7577–7603.
[arXiv]
[Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
Almost sure scattering for the energy-critical NLS with radial data below H1(R4). Comm. Partial Differential Equations
44 (2019), no. 1, 51–71.
[arXiv] [Journal] [MathSciNet]
R. Killip, S. Masaki, J. Murphy, and M. Visan,
The radial mass-subcritical NLS in negative order Sobolev spaces. Discrete Contin. Dyn. Syst.
39 (2019), no. 1, 553–583.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
Random data final-state problem for the mass-subcritical NLS in L2. Proc. Amer. Math. Soc.
147 (2019), no. 1, 339–350.
[arXiv] [Journal] [MathSciNet]
J. Murphy,
The nonlinear Schrödinger equation with an inverse-square potential. Nonlinear dispersive waves and fluids, 215–225, Contemp. Math.
725 (2019).
[pdf] [Journal] [MathSciNet]
B. Dodson and J. Murphy,
A new proof of scattering below the ground state for the non-radial focusing NLS. Math. Res. Lett.
25 (2018), no. 6, 1805–1825.
[arXiv] [Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
The initial-value problem for the cubic-quintic NLS with non-vanishing boundary conditions. SIAM J. Math. Anal.
50 (2018), no. 3, 2681–2739.
[arXiv] [Journal] [MathSciNet]
J. Lu, C. Miao, and J. Murphy,
Scattering in H1 for the intercritical NLS with an inverse-square potential. J. Differential Equations
264 (2018), no. 5, 3174–3211.
[arXiv]
[Journal] [MathSciNet]
B. Dodson and J. Murphy,
A new proof of scattering below the ground state for the 3d radial focusing cubic NLS. Proc. Amer. Math. Soc.
145 (2017), no. 11, 4859–4867.
[arXiv]
[Journal]
[MathSciNet]
R. Killip, S. Masaki, J. Murphy, and M. Visan,
Large data mass-subcritical NLS: critical weighted bounds imply scattering. NoDEA Nonlinear Differential Equations Appl.
24 (2017), no. 4, Art. 38, 33pp.
[arXiv] [Journal] [MathSciNet]
J. Murphy and F. Pusateri,
Almost global existence for cubic nonlinear Schrödinger equations in one space dimension. Discrete Contin. Dyn. Syst.
37 (2017), 2077–2102.
[arXiv]
[Journal]
[MathSciNet]
R. Killip, J. Murphy, M. Visan, and J. Zheng,
The focusing cubic NLS with inverse-square potential in three space dimensions. Differential Integral Equations
30 (2017), no. 3-4, 161–206.
[arXiv]
[Journal]
[MathSciNet]
B. Dodson, C. Miao, J. Murphy, and J. Zheng
The defocusing quintic NLS in four space dimensions. Ann. Inst. H. Poincaré Anal. Non Linéaire
34 (2017), no. 3, 759–787.
[arXiv]
[Journal] [MathSciNet]
R. Killip, J. Murphy, and M. Visan,
The final-state problem for the cubic-quintic NLS with non-vanishing boundary conditions. Anal. PDE
9 (2016), no. 7, 1523–1574.
[arXiv]
[Journal]
[MathSciNet]
J. Murphy,
The radial defocusing nonlinear Schrödinger equation in three space dimensions. Comm. Partial Differential Equations
40 (2015), no. 2, 265–308.
[arXiv]
[Journal]
[MathSciNet]
C. Miao, J. Murphy, and J. Zheng,
The defocusing energy-supercritical NLS in four space dimensions. J. Funct. Anal.
267 (2014), no. 6, 1662–1724.
[arXiv]
[Journal]
[MathSciNet]
J. Murphy,
The defocusing H1/2-critical NLS in high dimensions. Discrete Contin. Dyn. Syst.
34 (2014), no. 2, 733–748.
[arXiv]
[Journal]
[MathSciNet]
J. Murphy,
Intercritical NLS: critical Hs-bounds imply scattering. SIAM J. Math. Anal.
46 (2014), no. 1, 939–997.
[arXiv]
[Journal]
[MathSciNet]
J. Murphy,
Nonlinear Schrödinger equations at non-conserved critical regularity. Ph.D. Thesis (2014).
[pdf]
[MathSciNet]